$mathbb{Z}_2$-homology of weak $(p-2)$-faceless $p$-pseudomanifolds may be computed in $O(n)$ time

Abstract

We consider the class of weak $(p-2)$-faceless $p$-pseudomanifolds
with bounded boundaries and coboundaries.
We show that in this class the Betti numbers with $\mathbb{Z}_2$ coefficients
may be computed in time $O(n)$ and the $\mathbb{Z}_2$ homology generators
in time $O(nm)$ where $n$ denotes
the cardinality of the $p$-pseudomanifold on input and
$m$ is the number of homology generators.